5th International Conference on Durability of Concrete Structures Jun 30 Jul 1, 2016 Shenzhen Uniersity, Shenzhen, Guangdong Proince, P.R.China Effect of Fractal Dimension of Fine Aggregates on the Concrete Chloride Resistance W. Xue Department of Ciil Engineering and Architecture, Zhejiang Uniersity of Science and Technology J. Chen Institution of Structural Engineering, Zhejiang Uniersity ABSTRACT The relationship between fractal dimension of fine aggregates and the chloride resistance of concrete was inestigated in this study. Both concrete and mortar specimens were cast. Concrete specimens were in the same mix design as the mortar specimens except for the coarse aggregates. The specimens were diided into different groups based on the gradation of the fine aggregates. The chloride resistances of concrete specimens were tested by using the rapid chloride migration method. The results indicate that high olume fractal dimensions of fine aggregates hae positie impacts on the chloride resistance of concrete. The simplified calculating formulas were proposed. 1. INTRODUCTION Aggregate takes up 60% 90% of the total olume of concrete. Proper selection of aggregate particle size distribution affects the main properties of concrete: workability, strength, permeability, chloride resistance, and een the total cost of hardened concrete. Therefore, aggregate design is an essential part of concrete mix design. The fineness module (Mx) is widely used to describe the aggregate characters. Howeer, it is rough in describing the characters of the fine aggregates. Fractal dimension of the aggregate is recently adopted in aggregates researches. The fractal theory, which focused on the irregular geometric items, was established by Mandelbrot and so called fractal geometry (Mandelbrot, 1984). It was then deeloped quickly and extended to use in the researches on the other irregular or unstable problems in nature, such as the studies of soil particles and geotechnical materials (Lange, Jennings, & Shah, 1993; Saouma & Barton, 1994; Xie, 1997). Current researches reported that fractal alue of a certain object actually describes its complexity quantitatiely. It is the potential to connect the macro-performance with the microstructures by using this parameter. Concrete material is well known for its anisotropy. It could be attributed to the complexity of its microstructures, which is a kind of fractal system. The aggregates were composed of large numbers of particles in different sizes. The distribution of the particles is considered as a generalized fractal problem in mathematics (AASHTO, 1989). Current design standard only proide the size limitations on aggregates (ACI Committee 318 (ACI 318), 2005). In this study, the mass and olume fractal dimensions of the fine aggregates were calculated. By taking concrete and mortar durability experiments, the effects of fractal dimensions of fine aggregates on the chloride resistance of concrete were inestigated. The fractal dimension is suggested to be a design index in concrete mixtures. 2. FRACTAL DIMENSIONS The particle size (siee size) generates a distribution which could be described using a fractal method. In addition, the mass distribution (sieing ratio) and the olume architectures can both also be described by using fractal method as presented below. 2.1 Volume fractal dimension For the particles of size x, the distribution function could be written as Eq. (1): Fx ( ) = ( ) Nx N (1) where N(x) is the number of fine aggregates whose size are less than or equal to x. Since the size of fine aggregates could be classified as point problem, the fractal dimension N(x) could be calculated as Eq. (2), according to Xie (1997): Nx ( ) = N0 0 D (2) where x represents the imum size of the fine aggregate particles, N 0 is a constant, and D is the size fractal dimension alue. 89
90 5TH INTERNATIONAL CONFERENCE ON DURABILITY OF CONCRETE STRUCTURES Classifying the piled particles of the fine aggregates as a olume problem, the olume fractal character could be used to describe the oid filling capacity of those particles (Xu, 1991). The fractal dimension V(x) could be calculated as Eq. (3), comparing to Eq. (2), according to Xie (1997): Vx ( ) = V0 (3) where V(x) is the fractal olume and D is the olume fractal dimension. dv( x) = dv0 (4) M dpx ( ) dv = (5) 0 Based on the simultaneous Eqs (3 5), the fractal olume could be calculated using Eq. (6): Vx ( ) = 3 D D D 6 6 D D 6 D D D 3 min M x x min x x x (6) In addition, when numerous particles with different sizes are piled together, there is oid among them. The oid olume of the particles pile could be calculated using Eq (7): Table 1) using the automatic siee shaker. Then, the particles of different size were mixed following the designed distribution in Table 1. The imum size of fine aggregates is 4.75 mm. The oid olumes of each aggregate set were tested according to the standard (JGJ/T 70-2009, 2009). The olume fractal dimensions were calculated using Eq. (7) and presented in Table 2. Figure 1 shows a decreasing linear relationship between the olume fractal dimension alues D and oid olumes. An linear relationship between the percentage of oids and D could be obtained as Eq. (8): V oid % = -31.61 D + 113.58 (8) It may be explained that with the increase of olume fractal dimension, the filling capacity of particles also increases, which results in reduction of oid. Table 1. Fine aggregate particle size distribution. Accumulated siee ratio (%) Siee size (mm) I II III IV V VI VII 4.75 4 3 3 2 2 1 1 2.36 45 41 38 34 31 26 22 1.18 69 65 61 57 53 46 41 0.60 83 80 77 73 70 63 58 0.30 92 83 87 85 83 77 73 0.15 97 96 95 93 92 89 87 <0.15 100 100 100 100 100 100 100 V oid M V = M 3 D x = 1 6 D D γ = 1 0 6 D D 6 D D x min D 3 x x x min (7) Table 2. Fractal dimensions of fine aggregates. Groups q 0 (g/cm 3 ) f (g/cm 3 ) Void (%) D I 2.00 1.6393 18.03 2.6458 II 2.50 1.6667 33.33 2.5775 III 2.38 1.7544 26.32 2.7183 IV 2.33 1.7241 25.86 2.7429 V 2.70 1.8868 30.19 2.7040 VI 2.50 1.8519 25.93 2.7825 VII 2.33 1.7241 25.86 2.7980 where g is the compacted density and r 0 is the gross density of the particles pile. Proided the measured alue of V oid, x and x min of a certain pile of fine aggregates, the olume fractal dimension D could be calculated using Eq. (7). 3. RELATIONSHIP BETWEEN FRACTAL DIMENSIONS AND MORTAR/CONCRETE DURABILITY PERFORMANCE 3.1 Fine aggregates gradation Seen series of fine aggregate particle size distribution were designed in this study. All the fine aggregates were oen dried and sieed to different sizes (see in Figure 1. Relationship between D and oid%.
Effect of Fractal Dimension of Fine AGGREGATES on the Concrete Chloride RESISTANCE 91 3.2 Relationship between fractal dimensions and chloride resistance of mortar specimens Seen series in total of seen mortar specimens were tested for chloride resistant test. The mixture information of mortar specimens was presented in Table 3. Table 3. Mixture design of the mortar specimens (kg/m 3 ). Cement Fly ash Slag Sand Water Water reducer 313 102 137 629 176 12 All the specimens were kept in tap water under room temperature (aerage of 25 C) for 28 days. Then, the specimens were put into an artificial accelerating testing chamber and subjected to wet dry cycles for 60 days. Mangat and Gurusamy (1987) found a significant difference between the diffusion rates of chloride through the casting face and the bottom face (during casting) of the prism. To eliminate the casting effect, all the faces of the specimens for chloride resistant test were coated with epoxy except the top surface. The top surface is ertical to the casting direction. The specimens was under salt water spraying for 3 h (wet cycle) out of 48 h and, for the remaining 45 h, they were left in the ambient laboratory conditions at a temperature of 45 C (dry cycle). After 60 days cycling, the powder samples were drilled out from each specimen along the ingression direction. Three holes were drilled in dry condition using a 14-mm diameter rotary impact drill for each specimen. Powdered samples were taken at eery 5 mm depth. The chloride concentration profile of each powder sample was measured by using the potentiometric titration method. Preious research (Gao, 2008) indicates that diffusing dominate the chloride s moing inside concrete away from the surface more than 7 mm. In this study, the apparent chloride diffusion coefficient D a (square centimeter per second) was obtained by Fick s second law without the test data at the depth of 5 mm: Cxt (, ) = C 1 erf s 2 x D t a (9) where C(x,t) is the chloride concentration at depth x and age t; C s is the surface chloride concentration. The results are presented in Table 4 and Figure 2. Table 4. Apparent chloride diffusion coefficient ( 10 12 cm 2 /s). I II III IV V VI VII 6.03 11.30 6.08 5.13 5.37 4.55 4.91 Figure 2. Relationship between D and apparent chloride diffusion coefficient. D a = -21.6 D + 64.56 (10) It should be noticed that all the specimens were cast in same mixture design except for the fine aggregate gradation. Therefore, the difference of chloride resistant ability of the mortar specimens could be only attributed to the difference of the fine aggregate distribution. The results indicate mortar specimens with high D hae high chloride resistance. The difference of fine aggregate causes approximately 250% difference in the chloride resistant ability of mortar specimens. It may be explained that higher olume fractal dimension leads to higher compacting ability of the particles. It might complicate the transferring paths of the chloride ions. This might result in the reduction in the apparent chloride diffusion coefficients. 3.3 Relationship between fractal dimensions and chloride resistance in concrete specimens For concrete specimens, coarse aggregates take about half of the total olume. The chloride moing route in concrete is probably changed due to the existing of coarse aggregate. Therefore, the effect of fractal dimensions of fine aggregates on the chloride resistance of concrete is inestigated in this study. Four series in total of 12 concrete specimens were tested, and each series has three specimens. The fine aggregate distributions of each series are presented in Table 5, and the mixture is presented in Table 6. Only the fine aggregate distribution is the ariable parameter for all specimens. The mass and olume fractal dimensions were calculated using Eq. (7) and presented in Table 7. The specimens were prepared in the same way as the mortar specimens. After a 28-day curing period, the rapid chloride migration test method (CCES01-2004, 2005) was used to measure the chloride penetration depths of concrete specimens. The chloride diffusion coefficient D RCM
92 5TH INTERNATIONAL CONFERENCE ON DURABILITY OF CONCRETE STRUCTURES alues were calculated based on the measured chloride ingress depth (CCES01-2004, 2005): Th( x α x ) 6 d d D = 2.872 10 (11) RCM t α = 3.338 10 3 Th where T is the aerage temperature of the anticathode cell (K), h is the height of the specimen (mm), t is the testing duration (s), and x d is the aerage ingress depth (mm). Table 5. Fine aggregate particles distribution in concrete specimens. Accumulated siee ratio (%) Siee size (mm) I II III IV 4.75 3 10 10 5 2.36 11 13 25 20 1.18 20 24 26 30 0.6 41 69 43 70 0.3 70 71 89 91 0.15 98 96 90 92 <0.15 100 100 100 100 Figure 3. Relationship between D and oid% in concrete. Table 6. Mixture design of the mortar specimens (kg/m 3 ). C FA Sl S G W Admixture 313 102 137 629 1014 176 12 Table 7. Fractal dimensions of fine aggregates in concrete specimens. Series q 0 (g/cm 3 ) f (g/cm 3 ) Void (%) D I 2.6667 1.6129 39.52 2.3239 II 2.1137 1.7604 16.71 2.8058 III 2.8840 1.8025 37.50 2.4871 IV 2.6736 1.7856 33.21 2.5316 The concrete testing results shows the same trend as the mortar testing results (see in Figures 3 and 4), but the effect of fine aggregate on the chloride resistance of concrete specimens is een significant. The difference of fine aggregate causes approximately 300% difference in chloride resistant ability of concrete specimens. This result indicates the importance of olume fractal dimensions of fine aggregates for the chloride resistance of concrete. The relationship between V oid % or D RCM and D in the case of concrete is written as Eqs (12) and (13) based on the testing results: V oid % = -49.87 D + 158.26 (12) D RCM = -2.14 D + 6.44 (13) Figure 4. Relationship between D and D RCM. 4. CONCLUSION In this study, the relationship between fractal dimension of fine aggregates and chloride resistance of concrete was inestigated. The testing results indicated that with the increasing of D, the oids of the fine aggregates piles decrease, as well as the chloride moing ability in either the mortar specimens or the concrete specimens. The equations for the relationships between the oid olume, chloride resistance, and olume fractal dimension D in the case of mortar had been established by using fractal theory. In addition, equations for the relationship between oid olume, chloride resistance, and D were obtained in concrete. ACKNOWLEDGMENTS The research of this paper is supported by the National Natural Science Foundation of Zhejiang Proince, China (LQ16E080005), and Fund of Guangdong Proincial Key Laboratory of Durability for Marine Ciil Engineering (GDDCE15-10). REFERENCES AASHTO. (1989). Report of the joint task force on rutting. Washington, DC: AASHTO.
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